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Monday Week 2 Lecture

1. Monday Week 2 Lecture. Jeff Eldred Relativistic Kinematics, Retarded Potentials, Synchrotron Radiation. 2. Overview. Relativistic Kinematics Example of Neutrino Beams Part II: Retarded Time Retarded Time Potential from a moving point charge Lienard Wiechert Potentials

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Monday Week 2 Lecture

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  1. 1 Monday Week 2 Lecture Jeff Eldred Relativistic Kinematics, Retarded Potentials, Synchrotron Radiation

  2. 2 Overview • Relativistic Kinematics • Example of Neutrino Beams • Part II: Retarded Time • Retarded Time • Potential from a moving point charge • Lienard Wiechert Potentials • Power Radiated from a moving charge

  3. 3 Relativistic Decay

  4. Relativistic Decay Center of Mass Frame. Conservation of Momentum: Conservation of Energy: Solve for p, E:

  5. Relativistic Decay Solve for p, E: Boost into Lab Frame:

  6. Pion & Kaon Decays

  7. 7 Retarded Time

  8. Fields at the Speed of Light • Einsteinian causality requires that no information propagate faster than the speed of light . • The changes in E & B fields propagate at the speed of light, radiating outward from a changing source. • See Java Demo.

  9. Retarded Time • A point in space is affected by the E-fields originating from a source in the past, at a time called the retarded time. • In the past, the position of the source will have changed and that will in turn impact the time that should be evaluated.

  10. Retarded Time & Light Cone

  11. Retarded Potentials

  12. 12 Moving Point Charge

  13. Moving Point Charge Solve by change of variables:

  14. Change of Variables

  15. Moving Point Charge Potentials We have derived: A similar derivation shows that:

  16. Match what we found before? There is a trick we can use:

  17. Lienard-Wiechert Potentials Actually this form is valid even for point sources not moving in a straight line at constant velocity.

  18. Fields from a Point Charge

  19. 19 Power Radiated

  20. Power Radiated Radiation in reference frame in which Beta is small: Integrate over Poynting for radiation: Linear acceleration: Circular acceleration:

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